How to animate cvt belt as pulleys change size
The changes in a CVT belt ratio can be simulated using softbodies in Blender.

Details

Create a new blend file.
Add geometry for the pulleys and belt as shown in the animation.
Set the pulleys physics to act as collision.
Set the belt as a softbody.
Turn off gravity to prevent the belt from slipping.

It take 2 steps to animate the belt size change. First the belt needs to be fit to the pulleys. Then the pulley size can be animated with the belt keeping fit.

Animate the pulleys moving apart to the final location. The belt will stretch to fit the pulleys as they pull apart.
Animate the change in pulley size. The tension on the belt will ensure it stays close the pulleys as they change size.


The blend file is available here -